iSoul In the beginning is reality

The speed of spacetime

For each mode of travel there are four speeds to consider: the minimum speed, the typical speed, the maximum speed, and the speed of particular objects. The more that impediments to travel are removed (e.g., other objects, the topography, the network), the more that speed reaches free flow.

In transportation, the free flow speed is slower than the maximum speed. For example, the maximum speed for a highway vehicle might be determined by the fastest speed of a vehicle on the Bonneville Salt Flats. Or by the fastest speed at a NASCAR stock car race. These speeds would be much faster than what is safe on a highway. In physics, the free flow speed and the maximum speed are the same because of the principle of least action.

If there exists a speed that is constant for all particles or vehicles, then there is a way to relate the space and time coordinates of every event. Depending on whether this special speed is the minimum, the maximum, or the typical speed, there will be a kind of Lorentz transformation of the coordinates.

A coordinate system is a map for representing objects in space and/or time. The origin point of a coordinate system represents the reference point for the other points represented.

Maps may be static and represent a rest frame or they may be dynamic and change with their location as with GPS devices. For example, the origin point of a dynamic map may represent the location of a moving vehicle.

A spacetime coordinate system needs a way to relate spatial and temporal coordinates. The relation may be very particular, localized, and complex or it may be general, universal, and simple. The simplest relation between space and time is a constant. Such a constant represents a speed.

All maps have a scale, e.g., one centimetre represents 500 metres. A map with a reference speed also has a time scale, e.g., one centimetre represents one minute. To represent an arbitrary point in spacetime requires two maps: one for the space coordinates and the other for the time coordinates. These may be combined if different axes have different units. Or time coordinates may be put on a space map (and vice versa) as isoline plots, i.e., isochrones or isodistances.

The relation between the scale of space and the scale of time on two related maps is the speed that ties them together. That is the speed of spacetime.

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